I am doing the amount of permutations in the word trigonometry. For the expression, I wrote 12!/2!2!2!. I got 968003200. Is this correct? If not, should I use parenthesese? Thanks

Question

I am doing the amount of permutations in the word trigonometry.  For the expression, I wrote 12!/2!2!2!.  I got 968003200.  Is this correct? If not, should I use parenthesese? Thanks

drwls · Answer

There are 12 letters and 12 possible choices for the first letter, 11 for the second, etc. The number of ways of choosing them is 12!, which is 479,001,600. Some will be indistiguishable and should not be counted twice. Therefore 12! has to be divided by 2!2!2!= 8 since there are two t's, two r's and two o's. I agree with your formula but not with your number. The number I get is 59,875,200 distinct permutations.